Problem

Yomega ("The yo-yo with a brain") is constructed with a clever clutch mechanism in...

Yomega ("The yo-yo with a brain") is constructed with a clever clutch mechanism in its axle that allows it to rotate freely and "sleep" when its angular speed is greater than a certain critical value. When the yo-yo’s angular speed falls below this value, the clutch engages, causing the yo-yo to climb the string to the user’s hand. If the moment of inertia of the yo-yo is 7.4 × 10−5 kg· m2, its mass is 0.11 kg, and the string is 1.0 m long, what is the smallest angular speed that will allow the yo-yo to return to the user’s hand?